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TECHNICAL PAPERS

# Small Scale Modeling of Vertical Surface Jets in Cross-Flow: Reynolds Number and Downwash Effects

[+] Author and Article Information
K. Shahzad, D. J. Wilson

Department of Mechanical Engineering, University of Alberta, Edmonton, Alberta, Canada T6G 2G8

B. A. Fleck1

Department of Mechanical Engineering, University of Alberta, Edmonton, Alberta, Canada T6G 2G8brian.fleck@ualberta.ca

1

Corresponding author.

J. Fluids Eng 129(3), 311-318 (Aug 03, 2006) (8 pages) doi:10.1115/1.2427084 History: Received February 08, 2006; Revised August 03, 2006

## Abstract

Jet-crossflow experiments were performed in a water channel to determine the Reynolds number effects on the plume trajectory and entrainment coefficient. The purpose was to establish a lower limit down to which small scale laboratory experiments are accurate models of large scale atmospheric scenarios. Two models of a turbulent vertical surface jet (diameters $3.175mm$ and $12.7mm$) were designed and tested over a range of jet exit Reynolds numbers up to $104$. The results show that from Reynolds number 200–4000 there is about a 40% increase in the entrainment coefficient, whereas from Reynolds number 4000–10,000, the increase in entrainment coefficient is only 2%. The conclusion is that Reynolds numbers significantly affect plume trajectories when the model Reynolds numbers are below 4000. Changing the initial turbulence in the exit flow from 12% to 2% without changing its mean velocity profile caused a less than one source diameter increase in the final plume rise.

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Copyright © 2007 by American Society of Mechanical Engineers
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## Figures

Figure 1

Continuous downwash velocity distribution along the plume. Downwash velocity Wd decreasing with x as rising plume increases space for entrainment into bottom of bent-over plume.

Figure 2

Low pressure on the wall is induced as free stream fluid accelerates toward the jet centerline before it is entrained

Figure 3

Schematic view of the water channel facility, looking down through the free water surface

Figure 4

Contour profiles of average images for the source, produced from 200 (top) and from 1200 (bottom) consecutive images. M=4.0, Red=9100. The images are averages of 1∕30s video frames taken 1∕6s apart (6frames∕s), in a crossflow with velocity Ua=180mm∕s, which is 14 source diameters/s.

Figure 5

Concentration and contour profiles are shown together. Jet trajectory was determined by joining the peaks of these concentration profiles.

Figure 6

Comparison between experimental data and the momentum rise equation (Eq. 3) with no downwash correction for the large source diameter. The trajectory averaged entrainment coefficients, β, are much too large if no downwash correction is used.

Figure 7

Comparison between experimental data and the momentum rise equation (Eq. 3) with no downwash correction for the large source diameter. The trajectory averaged entrainment coefficients, β, are large but acceptable for this momentum ratio M=4 but the slope does not match well without a downwash correction.

Figure 8

Comparison between experimental data and the plume rise equation with downwash correction (Eq. 11). Wall wake decay exponent n=1∕3, B=0.20 at M=1.

Figure 9

Comparison between experimental data and the plume rise equation with downwash correction (Eq. 11). Wall wake decay exponent n=1∕2, B=0.20 at M=1.

Figure 10

Large source comparison between experimental data and the plume rise equation with downwash correction (Eq. 11). B=0.43

Figure 11

Small source comparison between experimental data and the plume rise equation with downwash correction (Eq. 11), B=0.50

Figure 12

Effect of Red on entrainment coefficient normalized by the high jet exit Reynolds number entrainment coefficient β∞ at the largest measured Red for that M

Figure 13

Entrainment coefficient decreases as M increases. Previous measurements (5) shown as solid circle; present study as solid squares.

Figure 14

Effects of Red on plume rise. The curve given is based on Eq. 16.

Figure 15

Effects of jet exit turbulence on the plume trajectory at low density-weighted velocity ratio M

Figure 16

Effects of jet exit turbulence on the plume trajectory at high density-weighted velocity ratio M

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